If you were represented by a union with a collective bargaining agreement in place, you may have rights to appeal your termination. Contact your union rep right away.
If no union, then you were an "at will" employee and your employer was free to exercise the power of termination for any reason that is not unlawful. The reasons you have cited here as underlying your termination are not unlawful. In at will employment, the employer's reasons for termination are not required to be true or correct,nor must the employer conduct an investigation or provide an opportunity to the employee to defend.
Gossip and shop talk is an unfortunate part of community life and your employer cannot be successfully sued for the inevitable chatter and speculation following your termination. Specific false statements of fact by management to 3rd parties that cause you economic damages may be actionable, but these are difficult and expensive cases with very exacting legal procedures. Talk with a local attorney about your prospects before you initiate such action. In many cases, the likely outcome cannot justify the investment of money, time, effort, and emotional stamina.
If you applied for unemployment benefits and your employer contested your claim, the administrative hearing process may serve as a vehicle by which you can obtain additional information about your employer's factual basis for concluding that you were the thief. That information may suggest some additional worthwhile approaches to this matter.
My responses to questions on Avvo are never intended as legal advice and must not be relied upon as legal advice. I give legal advice only in the course of an attorney-client relationship. Exchange of information through Avvo's Questions forum does not establish an attorney-client relationship with me. That relationship is established only by individual consultation and execution of a written agreement for legal services.